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Problem $19$ for Reference

$19.$ Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all$-$equity firm that specializes in this business. Suppose Harburtin$$s equity beta is $0\mathrm{.}85,$ the risk$-$free rate is $4\%,$ and the market risk premium is $5\%.$ If your firm$$s project is all$-$equity financed, estimate its cost of capital.

Consider the setting of Problem $19.$ You decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second firm, Thurbinar Design, which is also engaged in a similar line of business. Thurbinar has a stock price of $$20$ per share, with $15$ million shares outstanding. It also has $$100$ million in outstanding debt, with a yield on the debt of $4\mathrm{.}5\%.$ Thurbinar$$s equity beta is $1\mathrm{.}00.$

a$.$ Assume Thurbinar$$s debt has a beta of zero. Estimate Thurbinar$$s unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar$$s unlevered cost of capital.

b$.$ Estimate Thurbinar$$s equity cost of capital, and assume its debt cost of capital equals its yield. Based on these results, estimate Thurbinar$$s unlevered cost of capital.

c$.$ Explain the difference between your estimates in parts $($a$)$ and $($b$).$

d$.$ You decide to average your results in parts $($a$)$ and $($b$),$ and then average this result with your estimate from Problem $19.$ What is your estimate for the cost of capital of your firm$$s project?